Research Of Finite Element Method–Mode Matching Method For Passive Microwave Devices

When dealing with the truncation surface, the absorb boundary conditions(ABC) is currently used in the Microwave Tube Simulator Suite(MTSS). But for meshing, it requires that the nearest distance between the absorption boundary and the scatter must be greater than or equal to half a wavelength of the electromagnetic wave. Otherwise, because of the existence of port impedance and dispersion phenomena, ABC has limitation when dealing with multi- mode problems. This thesis concentrates on the application of a hybrid algorithm combining finite ele ment method with mode matching method(FEM-MMM). FEM-MMM can be used to deal with the truncated boundary of models in MTSS. Mode analysis can deal with the multi- mode problems. With the help of normal modes, the S parameters and the coefficients of vector basis can be calculated directly by solving the finite element equations which are obtained from the weak statement for the vector Helmholtz equation. FEM-MMM can narrow the distance between truncation surface and the target area. Thus, the computational domain and the solving time will decrease.This thesis focuses on the FEM-MMM, ABC and the weak statement for the vector Helmholtz equation. The main works and innovative points are as follows:1. In chapter two, the theories of finite element are systematically introduced. The large generalized eigenvalue problem is studied and analyzed. This paper gives an algorithm for solving the large generalized eigenvalue problem by applying related theories. Furthermore, after the comparison between the computed values and the theoretical values, it is shown that the maximum error is-1.0354%. We analysis the rectangular waveguide based on the mode analysis method and draw the mode chart using numerical method in chapter three.2. Chapter four begins with the research of FEM-MMM for passive microwave devices and the development of the weak statement for the vector Helmholtz equation. Chapter four first analyzes the situation of one-port network and develops the finite element equations which are excited by dominant mode and arbitrary function, respectively. We analyze the situation of multiport excitation and derive the finite element equations of multiport with arbitrary function excitation. At last, to make FEM-MMM more applicable the finite element equations of FEM-MMM in conjunction with ABC are derived. This thesis realizes dominant mode excitation based on numerical integration. We can get the S parameter and vector basis interpolation coefficient directly by solving the above-mentioned finite element equations.3. In chapter five, rectangular waveguide, T-shape waveguide and pillbox windows are calculated and analyzed. The S parameters calculated in this paper are compared with the S parameters calculated by HFSS and CST and the results are in good agreement. The analysis of results shows that this algorithm is reliable and effective. The electric field within the solution area is reconstructed by using the interpolation coefficients of the vector basis functions. The electric field nephogram of various devices were drawn by post-processing technology in Appendix 1, Appendix 2 and Appendix 3, respectively.4. The excitation in HFSS can only be chosen either the dominant mode or a certain high-order mode. This paper puts forward a innovative way to set the excitation with arbitrary function. And this arbitrary function should be piecewise-continuous and well-behaved function in the field of definition. By using the method of mode analysis, the arbitrary function can be expanded into the summation of finite orthogonal mode field. Then the arbitrary function can be added as excitation by substituting the mode into boundary conditions in conjunction with Maxwell equations.